As stated by Brown, R. F., ed. in mathematics, a fixed point theorem is a result saying that a function F will have at least one fixed point a point for which, under some conditions on that can be stated in general terms. Various issues arise in day-to-day life in various spheres of science and other related branches of studies like Management, Economics, Medical, Engineering, Chemical Sciences, Physics, etc. The Fixed Point concept is important to numerous theoretical and implemented fields, including variation and linear inequalities, approximation concept, non-linear evaluation, integral and differential equations, inclusions, the dynamical structure concept, mathematics of fractals, mathematical economics and mathematical modeling. The topological Fixed Point theory is a systematically advanced area that may be effectively implemented in lots of branches of mathematics, mathematical physics, and herbal science. Numerous problems occurring in various branches of mathematics, differential equations, optimization theory and variation evaluation may be modeled via way of means of the equation u = Du, where D is a non-linear operator described on a Metric Space. The answers to this comparison are referred to as fixed points of D. In 1906, the French mathematician Frechet presented Metric Spaces which helped in the development of Fixed Point theory. The first Fixed Point Theorem in Metric Space for contraction mappings was proved by a great mathematician, Banach, in 1922. This theorem.is well-known as Banach’s Fixed Point Theorem or the Banach Contraction Principle. At present, this proof has become a well-known and influential device in explaining existing issues in numerous branches of mathematical evaluation. Due to the effortlessness and value of this fundamental theorem, it has applications in numerous branches of mathematical evaluation. In 1968, Kannan added a contractive situation that controlled a distinctive Fixed Point like that of Banach. However, in contrast to the Banach situation, Kannan proved that there are mappings that have a discontinuity in their domain but have Fixed Point, even though such mappings are continuous at their Fixed Point. Brouwer’s Fixed Point Theorem. Assures that any endless conversion on the closed ball in Euclidean space has a fixed point.
Author(s) Details:
Arti Saxena,
School of Engineering and Technology, Manav Rachna International Institute of Research and Studies Faridabad, Haryana, India.
Poonam Rani,
Department of Humanities and Applied Sciences, Echelon Institute of Technology, Faridabad, Haryana, India.
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